## Definition ## A __commutative Heyting reciprocal ring__ is a [[Heyting reciprocal ring]] $(A, +, -, 0, \cdot, 1, #)$ with a commutative identity for $\cdot$: $$m_\kappa:\prod_{(a:A)} \prod_{(b:A)} a\cdot b = b\cdot a$$ ## Properties ## Every commutative Heyting reciprocal ring is a commutative [[Heyting division ring]]. ## Examples ## * The [[rational numbers]] are a commutative Heyting reciprocal ring. * Every [[commutative discrete reciprocal ring]] is a commutative Heyting reciprocal ring. * Every [[commutative Heyting division ring]] is a commutative Heyting reciprocal ring. * Every [[Heyting field]] is a commutative Heyting reciprocal ring. ## See also ## * [[commutative ring]] * [[commutative reciprocal ring]]